I'm knitting a purse and the instructions say to "sl3 at the end of each row" (purl stitches) in the flap (garter stitch). What do I do with the yarn? How do I carry it to the end of the row? And why does each side look different?

You may be doing an I cord edge, where the 3 sts and the carried yarn form a sort of cord. Slip the sts purlwise with the yarn in front, then turn and knit. The yarn may be slightly loose, but after a few rows will turn under and form the I cord.